English

On Alternating 6-Cycles in Edge-Coloured Graphs

Combinatorics 2025-05-16 v1 Discrete Mathematics

Abstract

In this short note, we use flag algebras to prove that the number of colour alternating 6-cycles in a red/blue colouring of a large clique is asymptotically maximized by a uniformly random colouring. This settles the first open case of a problem of Basit, Granet, Horsley, K\"undgen and Staden.

Keywords

Cite

@article{arxiv.2505.09809,
  title  = {On Alternating 6-Cycles in Edge-Coloured Graphs},
  author = {Hao Chen and Jonathan A. Noel},
  journal= {arXiv preprint arXiv:2505.09809},
  year   = {2025}
}

Comments

19 pages, 2 figures

R2 v1 2026-06-28T23:33:43.848Z